Kerr optical frequency combs
Optical frequency combs are sets of regularly spaced spectral lines in the ultraviolet, visible, or infrared ranges. They have for long been generated with mode-locked ultrafast lasers, as periodic trains of ultrashort laser pulses yield such equidistant lines in the spectral domain. Many applications can benefit from these combs: fundamental physics, time-frequency metrology, navigation systems, spectroscopy, sensing, or ultralow phase noise microwave and terahertz generation. An interesting method has been demonstrated recently for the generation of these combs, and it relies on the hyperparametric excitation of the WGMs of an ultra-high Q monolithic resonator. In these resonators, the small volume of confinement, high photon density, and long photon storage time (proportional to the quality factor Q) induce a very strong light-matter interaction. Depending on the dielectric material, this strong coupling can generate a highly efficient four-wave mixing (FWM), where two pump photons are transformed into two sideband photons through the Kerr nonlinearity. Provided that the pump is powerful enough, an optical-frequency comb, sometimes referred to as a Kerr comb, is generated through a cascaded creation of such sideband photons, resulting from a huge sum of weighted interactions involving any four photons fulfilling energy and angular momentum conservation requirements.
From the experimental side, we actively work on the Kerr comb generation using different types of resonators and pump conditions. We are in particularly interested in solutions that are able to provide the highest coherence in view of applications, and this is why we particularly focus on the so-call primary combs, characterized by a tunable intermodal frequency as a function of the pump wavelength. The main solutions in this case are ultra-pure microwave generation and WDM optical communications. We explore as well other solutions such as chaotic combs, which have potential applications as a coherent broadband sources. The figure shows a resonator and its taper before coupling (here, they are about a mm apart): evanescent coupling occurs when the taper is approached at sub-wavelength distance (typically, <1 μm), and a Kerr comb can be generated beyond a certain pump threshold. It should be noted that the taper coupling is indeed suitable for laboratory experiments and academic research (coupling efficiency >99%), but not for industrial applications because of its poor mechanical robustness. For application-oriented projects, we use systematically use instead a prism-coupling configuration which features slightly lower coupling efficiency (~80%), but significantly higher mechanical robustness, immunity to vibrations, and longevity.
From the theoretical side, we have indeed pioneered the two models that are used today for the analysis and understanding of Kerr combs, namely the modal model (with the NASA Jet Propulsion Lab) and the spatiotemporal model, also referred to as Lugiato-Lefever model (with Univ. Maryland Baltimore County. We investigate extensively the nonlinear dynamics of these combs in order to understand their stability properties. The objective here is to identify the best kind of combs depending on the targeted application. Possible solutions include Turing rolls, chaos, bright solitons, soliton molecules (bound states), dark solitons, platicons/flaticons, and breathers (periodic and chaotic). We currently undertake this research in collaboration with applied mathematicians who are particularly interested by the normal form theory associated with the Lugiato-Lefever equation. We also use the experimental results as a method to confirm or infirm the predictions from the models, as well as a tool to allow for their improvement.
Further reading:
– Chembo, Strekalov and Yu (2010)
– Pfeifle et al. (2015)
– Chembo (2016)
– Lin, Coillet & Chembo (2017)
– Pasquazi et al. (2018)
Raman optical frequency combs
In amorphous media or centrosymmetric crystals, the leading nonlinear effects are related to the third-order susceptibility. In this case, the light-matter interaction in the WGM resonator generally yields either a Kerr or a Raman comb when the resonator is pumped above a certain threshold. On the one hand, Kerr combs are highly coherent and originate from the quasi-instantaneous electronic response of the bulk medium to the laser excitation. On the other hand, Raman combs result from the delayed molecular response of the host medium to the laser excitation. These combs are can be either coherent or incoherent, and result from the cascaded excitation of longer wavelength modes (or Stokes lines) far away from the pump, typically at 10 THz and its harmonics.
A key objective is to achieve mode-locking with such Raman combs, which are characterized by a wide frequency span (tens of THz) and very low threshold powers (down to sub-mW). However, overall coherence is not easy to obtain and maintain, because the Raman nonlinearity spans over such a large frequency span. The main issue becomes dispersion, since the very large action range of Raman scattering forbids the crude approximation that consists of considering only low-order dispersion coefficients. The transverse multimode nature of the resonator allows as well for many combinations in the energy diagram ruling the interaction between the photons and the optical phonons. Accordingly, the number of degrees of freedom becomes so large that modelling becomes particularly challenging. Nevertheless, we have successfully achieved this task using a spatiotemporal model similar to the one used in supercontinuum generation. From our on-going research activity, we expect that dispersion management will provide useful degrees of freedom for the purpose of tailoring these Raman combs for various applications.
Further reading:
– Lin, Coillet & Chembo (2017)
Brillouin optical frequency combs
Stimulated Brillouin scattering is a nonlinear optical process resulting from the coherent interaction of light and acoustic waves (or acoustic phonons). It is usually related to the effect of electrostriction and gives rise to inelastic light backscattering with a Doppler downshift related to the acoustic phonon frequency. This downshift can be calculated from the elastic constants of the material, ans is usually of the order of 10 GHz. Beyond a given threshold, a Brillouin line is excited if energy and momentum conservation rules are respected, and further increase of the pump power leads to a cascade of higher-order Brillouin lines in the spectral domain. The figure shows a mm-size WGM resonator coupled with a red laser using a prism coupler.
The specific advantage of Brillouin lasing is that its characteristic frequency shift falls close to the X-band (8-12 GHz), which is used for various applications in microwave photonics. Moreover, the Brillouin gain can be very narrow (down to few tens of kHz), and this is a particularly rare feature in the optical domain since it corresponds to a Q factor of about ten billion at telecom wavelengths. Therefore, this effect has a strong potential for ultra-pure microwave generation, provided that the Brillouin gain is aligned with a ultra-high Q WGM resonance. The figure shows experimental measurements showing the onset of the first and second order thresholds for stimulated Brillouin scattering. The slope efficiency between both thresholds reaches 35%, thereby indicating a good energy conversion for microwave generation. It is also oteworthy that the very different multi-resonant and phase matching conditions required by Brillouin, Raman and Kerr interactions have made it difficult to excite them simultaneously. However, the specific advantage of monolithic WGM resonators is that their modal structure can allow to satisfy all these requirements at once. We have already shown that crystalline WGM resonators are ideal platforms in order to investigate the complex interplay of these three fundamental interactions when excited simultaneously. We have developped a full spatiotemporal model which provides an insightful understanding about these complex scattering phenomena and their mutual interactions.
Further reading:
– Lin, Coillet & Chembo (2017)